• 품질경영학회지
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• 제31권4호
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• pp.164-175
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• 2003

This paper investigates bootstrap confidence intervals of the process capability index(PCI) based on the expected loss derived from the empirical distribution function(EDF). The PCI based on the expected loss is too complex to derive its confidence interval analytically, so the bootstrap method is a good alternative. We propose three types of the bootstrap confidence interval; the standard bootstrap(SB), the percentile bootstrap(PB), and the acceleration biased­corrected percentile bootstrap(ABC). We also perform a comprehensive simulation study under various process distributions, in order to compare the accuracy of the coverage probability of the bootstrap confidence intervals. In most cases, the coverage probabilities of the bootstrap confidence intervals from the EDF PCI turned out to be more accurate than those from the PCI based on the normal distribution. It is expected that the bootstrap confidence intervals from the EDF PCI can be utilized in real processes where the true distribution family may not be known.

• Communications for Statistical Applications and Methods
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• 제12권1호
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• pp.71-86
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• 2005

Testing for normality has always been an important part of statistical methodology. In this paper a test statistic for multivariate normality is proposed. The underlying idea is to investigate all the possible linear combinations that reduce to the standard normal distribution under the null hypothesis and compare the order statistics of them with the theoretical normal quantiles. The suggested statistic is invariant with respect to nonsingular matrix multiplication and vector addition. We show that the limit distribution of an approximation to the suggested statistic is representable as the supremum over an index set of the integral of a suitable Gaussian process.

• Communications for Statistical Applications and Methods
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• 제29권3호
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• pp.333-351
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• 2022

The skew-t distribution is an attractive family of asymmetrical heavy-tailed densities that includes the normal, skew-normal and Student's-t distributions as special cases. In this work, we propose an EM-type algorithm for computing the maximum likelihood estimates for skew-t linear regression models with censored response. In contrast with previous proposals, this algorithm uses analytical expressions at the E-step, as opposed to Monte Carlo simulations. These expressions rely on formulas for the mean and variance of a truncated skew-t distribution, and can be computed using the R library MomTrunc. The standard errors, the prediction of unobserved values of the response and the log-likelihood function are obtained as a by-product. The proposed methodology is illustrated through the analyses of simulated and a real data application on Letter-Name Fluency test in Peruvian students.

• 품질경영학회지
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• 제41권2호
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• pp.233-248
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• 2013

Purpose: This study develops heuristic process capability indices (PCIs) using distribution-decomposition methods and evaluates the performances. The heuristic methods decompose the variation of a quality characteristic into upper and lower deviations and adjust the value of the PCIs using decomposed deviations in accordance with the skewness. The weighted variance(WV), new WV(NWV), scaled WV(SWV), and weighted standard deviation(WSD) methods are considered. Methods: The performances of the heuristic PCIs are investigated under the varied situations such as various skewed distributions, sample sizes, and specifications. Results: WV PCI is the best under the normal populations, WSD and SWV PCIs are the best under the low skewed populations, NWV PCI is the best under the moderate and high skewed populations. Conclusion: Comprehensive analysis shows that the NWV method is most adequate for a practical use.

• 한국농공학회지
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• 제18권4호
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• pp.4232-4241
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• 1976

This study was carried out to clarify the stochastic characteristics of monthly rainfalls and to select a proper model for generating the sequential monthly rainfall amounts. The results abtained are as follows: 1. Log-Normal distribution function is the best fit theoretical distribution function to the empirical distribution of monthly rainfall amounts. 2. Seasonal and random components are found to exist in the time series of monthly rainfall amounts and non-stationarity is shown from the correlograms. 3. The Monte Carlo model shows a tendency to underestimate the mean values and standard deviations of monthly rainfall amounts. 4. The 1st order Markov model reproduces means, standard deviations, and coefficient of skewness with an error of ten percent or less. 5. A correlogram derived from the data generated by 1st order Markov model shows the charaterstics of historical data exactly. 6. It is concluded that the 1st order Markov model is superior to the Monte Carlo model in their reproducing ability of stochastic properties of monthly rainfall amounts.

• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.1-10
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• 1999

Table of the empirical quantiles for the well known Shapiro-Francia W' goodness of fit statistic is produced which is more accurate than the existing ones. Prediction equation for the quantiles of W' statistic for sample sizes 30 or more we developed. The process of computing the expected values for the standard normal variate is discussed. This work is intended to make the Shapiro-Francia W' statistic more accessible to the practitioner.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2000년도 추계학술발표회 논문집
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• pp.187-191
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• 2000

In the analysis of repeated measurements, multivariate regression models that account for the correlations among the observations from the same subject are widely used. Like the usual univariate regression models, these multivariate regression models also need some model diagnostic procedures. In this paper, we propose a simple graphical method to detect outliers and to investigate the goodness of model fit in repeated measures data. The graphical method is based on the quantile-quantile(Q-Q) plots of the $X^2$ distribution and the standard normal distribution. We also propose diagnostic measures to detect influential observations. The proposed method is illustrated using two examples.

• 응용통계연구
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• 제32권1호
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• pp.99-109
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• 2019

비선형 시계열인 확률계수 자기회귀(random coefficient autoregressive; RCA) 모형에 대하여 여러 가지 방법을 이용한 추정량의 신뢰구간 비교하였다. RCA 모형에 대하여 자료의 분포를 가정하지 않아도 되는 Quasi 스코어 추정량과 Huber, Tukey, Andrew, Hempal 4가지 유계함수를 이용한 M-Quasi 스코어 추정량을 제시하였다. 이러한 추정량에 대하여 표준 붓스트랩 방법, 백분위수 붓스트랩 방법, 스튜던트화 붓스트랩 방법, 하이브리드 붓스트랩 방법을 이용한 신뢰구간을 구하였다. 모의실험을 통하여 RCA 모형의 오차항의 분포가 정규분포, 오염정규분포, 이중지수분포를 따를 때 Quasi 스코어 추정량과 M-Quasi 스코어 추정량들의 근사적 신뢰구간과 네가지 붓스트랩 방법을 이용한 신뢰구간을 비교하였다.

• 한국한의학연구원논문집
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• 제14권2호
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• pp.87-91
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• 2008

Background and Purpose: The purpose of this study was investigate statistical validities of previously reported articles that used various statistical techniques such as t-test and analysis of variance. Methods: To analyze the statistical procedures, 66 original articles using those statistical methods were selected from "Korean Journal of Oriental Medicine(KJOM)" published from 1995 to 2007. Results: Twenty-one articles(32%) did not report correct p-values, 33 articles(50%) used mean${\pm}$standard error(mean${\pm}$SE) and 11 articles(l7%) used mean${\pm}$standard deviation(mean${\pm}$SD). Fifty-two articles(95%) of 55 ones which were tested for normal distribution made an error in describing normal distribution. Seventeen articles misused t-test and 12 articles did not carry out the multiple comparison. Conclusions: The training of researchers with clinical statistics or the participation of statisticians in research design will reduce the significant errors in statistical interpretation of the results.

• 산업경영시스템학회지
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• 제31권4호
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• pp.134-139
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• 2008

Most approaches for continuous review inventory problem need tables for loss function and cumulative standard normal distribution. Furthermore, it is time-consuming to calculate order quantity (Q) and reorder point (r) iteratively until required values are converged. The purpose of this paper is to develop a direct method to get the solution without any tables. We used approximation approaches for loss function and cumulative standard normal distribution. The proposed method can get the solution directly without any iterative procedure for Q, r and without any tables. The performance of the proposed approach is tested by using numerical examples. The budget constraint of this paper assumes that purchasing costs are paid at the time an order is arrived. This constraint can be easily replaced by capacity constraint or budget constraint in which' purchasing costs are paid at the time an order is placed.